In this tool we explore how mathematics tasks can be used to connect student learning to the world of work. There is one tool but three suggested sample tasks that can be used with the same tool. When using this tool select the sample tasks that would be most suitable for the teachers involved. For example, if you are working with teachers whose students are most likely to be motivated by tasks set in the world of finance then use the first task suggested here. For those with an interest in design or writing then the other two sample tasks may be useful.

The tool provides an opportunity to explore classroom activity set in a world of work context. All the teachers may explore the same task or small groups might work with different tasks leading to a more general final discussion.

Introduce the session by clarifying that the aim is to explore how we might use tasks set in the world of work to stimulate mathematical activity.

Give pairs of teachers Handout 1, which asks questions about the likely responses of students to the mathematical activity they will engage in. Each pair will also need one of the tasks (Handout 2, 4 or 6) together with the appropriate Teacher Notes (Handout 3, 5, or 7).

Ask them to work through their task imagining how their students would respond. They should then fill in the Handout 1: Student responses to the task. This includes the questions:

What mathematical learning are students likely to take away from this task?

What difficulties might they have with (a) understanding what mathematics is needed and (b) using mathematics to model the situation?

How well will this activity work for students in terms of bringing the world of work into the classroom? Why?

Task 1: Mathematics in banking (Handout 2: Mathematics in the world of work – Insurance)

Lesson plan (Handout 3: Working in insurance: teacher notes).

There is a downloadable spreadsheet that you might use with this task.

Task 2: Mathematics in architecture (Handout 4: Mathematics in the world of work – Architecture)

Lesson plan (Handout 5: Working in architecture: teacher notes)

There is a video about the work of an architect that you could use in conjunction with this task. Ask teachers to think about the ways in which this video might be used a) as stimulus material for a mathematics inquiry and b) as a way to bring the world of work into the mathematics classroom.

Task 3: Mathematics in journalism (Handout 6: Mathematics in the world of work: Journalism)

Lesson plan (Handout 7: Working in journalism: teacher notes).

As a group, discuss your responses (written on Handout 1) and consider how students’ predicted responses might influence the ways in which teachers would plan to implement the task in the classroom. Try to make a summary of the mathematical learning that teachers think would occur.

Now introduce the modelling cycle (OECD, 2013) that is used to explore students’ mathematical activity in the PISA assessment framework (see diagram below). Check that everyone understands the key mathematical processes and has considered these in relation to their responses to the question “What mathematical learning are students likely to take away from this task?”

Wake (2015) writes:

“the important processes as one moves from a contextual to a mathematical world and back again are:

formulating—in which relevant mathematics that can lead to a solution, or sense-making, of the problem is identified. An appropriate mathematical structure and a representation(s) of this is developed by making simplifying assumptions and identifying variables;

employing—involves mathematical reasoning that draws on a range of concepts, procedures, facts and tools to provide a mathematical solution;

interpreting and evaluating—involves making sense, and considering the validity, of the mathematical results/solution obtained in terms of the context in which the problem situation arises.

The cyclical representation of this overall process provides for the expectation that a refinement, or complete rethink, of the mathematical structure representing the real world situation may be desired, or even necessary. It is also important to bear in mind that progression around the cycle is not necessarily entirely one way, as there may be the need to refine thinking at any stage as the potential effects of decisions being taken become apparent and need modification as one proceeds.”

Spend some time thinking about how the task(s) that teachers have considered will facilitate student engagement with these processes. Consider how an inquiry approach would involve students in exploring the effects of making different assumptions on answers/outcomes.

This type of mathematical thinking is very important in workplace situations. As Wake (2015) writes,

“Fundamental to understanding that underpins successful numerate activity in such cases (workplaces), is the development of insight into the interplay between variation of a factor in the reality and a factor in the mathematics or vice versa. The word interplay has been chosen with particular care here to embody ideas of reciprocal and mutual action and reaction. Critical inquiry is essential in the process of developing insight into such couplings and questions that, for example, have as their stem, “what if …..?” need to be considered.”

For example, in the different tasks presented here, consider the following “what if…..” questions:

Task 1: What if …different interest rates are used? …interest is compounded more frequently? … each year a small amount of money is removed from the account?

Task 2: What if … there were more spaces for motorbikes? … there were more spaces for disabled people? … more space was required for each car?

Task 3: What if … there were more/fewer people per unit area? … we changed our estimates for the dimensions of the space we are considering?

Discuss how the approach suggested here reflects mathematical ways of working in the world of work.

Ask teachers to develop a plan for a lesson perhaps modifying the one provided in order to take into account some of the things they have thought about. They could do this within the session, if you have time, or later.

Bring the group together to think about a research question they might want to pursue, such as, for example, the effectiveness of a sample task that they have discussed in bringing the world of work into the classroom.

Ask the teachers to agree on a task that they will use with a class before the next session. When they teach the task, they should focus on their research question and reflect on what happens in the classroom. They should be ready to report back on their findings to the group next time. Handout 8: Task reflection may be useful in supporting them with their reflections.

Acknowledgement & Copyright

The content of the mascil toolkit was developed by the mascil team at the University of Nottingham, UK.

The development of the concept of the mascil toolkit was led by the University of Nottingham, UK in discussion with the Universities of Jaen (ES) and Utrecht (NL) and the Pädagogische Hochschule, Freiburg (DE).

The mascil project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 320 693